%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU521^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:01:49 PM UTC 2025 % Result : Theorem 5.02s 5.19s % Output : Proof 5.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SEU521^2 : TPTP v9.2.0. Released v3.7.0. % 0.14/0.16 % Command : duper %s % 0.17/0.37 % Computer : n018.cluster.edu % 0.17/0.37 % Model : x86_64 x86_64 % 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.37 % Memory : 8042.1875MB % 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.37 % CPULimit : 300 % 0.17/0.37 % WCLimit : 300 % 0.17/0.37 % DateTime : Fri Oct 3 05:52:53 EDT 2025 % 0.17/0.37 % CPUTime : % 5.02/5.19 SZS status Theorem for theBenchmark.p % 5.02/5.19 SZS output start Proof for theBenchmark.p % 5.02/5.19 Clause #0 (by assumption #[]): Eq (Eq powersetAx (∀ (A B : Iota), Iff (in B (powerset A)) (∀ (Xx : Iota), in Xx B → in Xx A))) True % 5.02/5.19 Clause #1 (by assumption #[]): Eq (Not (powersetAx → ∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True % 5.02/5.19 Clause #2 (by clausification #[1]): Eq (powersetAx → ∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) False % 5.02/5.19 Clause #3 (by clausification #[2]): Eq powersetAx True % 5.02/5.19 Clause #4 (by clausification #[2]): Eq (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) False % 5.02/5.19 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in B (powerset (skS.0 0 a)) → in Xx B → in Xx (skS.0 0 a))) True % 5.02/5.19 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset (skS.0 0 a)) → in Xx B → in Xx (skS.0 0 a)) False % 5.02/5.19 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 5.02/5.19 Eq (Not (∀ (Xx : Iota), in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a))) True % 5.02/5.19 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 5.02/5.19 Eq (∀ (Xx : Iota), in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → in Xx (skS.0 1 a a_1) → in Xx (skS.0 0 a)) False % 5.02/5.19 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 5.02/5.19 Eq % 5.02/5.19 (Not % 5.02/5.19 (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → % 5.02/5.19 in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 5.02/5.19 True % 5.02/5.19 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 5.02/5.19 Eq % 5.02/5.19 (in (skS.0 1 a a_1) (powerset (skS.0 0 a)) → % 5.02/5.19 in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (skS.0 0 a)) % 5.02/5.19 False % 5.02/5.19 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (powerset (skS.0 0 a))) True % 5.02/5.19 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (skS.0 0 a)) False % 5.02/5.19 Clause #13 (by clausification #[0]): Eq powersetAx (∀ (A B : Iota), Iff (in B (powerset A)) (∀ (Xx : Iota), in Xx B → in Xx A)) % 5.02/5.19 Clause #14 (by forward demodulation #[13, 3]): Eq True (∀ (A B : Iota), Iff (in B (powerset A)) (∀ (Xx : Iota), in Xx B → in Xx A)) % 5.02/5.19 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (in B (powerset a)) (∀ (Xx : Iota), in Xx B → in Xx a)) True % 5.02/5.19 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (in a (powerset a_1)) (∀ (Xx : Iota), in Xx a → in Xx a_1)) True % 5.02/5.19 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) True) % 5.02/5.19 Clause #23 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True) % 5.02/5.19 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 5.02/5.19 Clause #25 (by superposition #[24, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Or (Eq (in a (skS.0 0 a_1)) True) (Eq False True)) % 5.02/5.19 Clause #28 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 5.02/5.19 Clause #29 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) False % 5.02/5.19 Clause #34 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Eq (in a (skS.0 0 a_1)) True) % 5.02/5.19 Clause #35 (by superposition #[34, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True) (Eq False True) % 5.02/5.19 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 5.02/5.19 Clause #38 (by superposition #[37, 29]): Eq True False % 5.02/5.19 Clause #41 (by clausification #[38]): False % 5.02/5.19 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------